There could still be a persistence-based cosmological argument even if there were existential inertia

Suppose that today at noon, Felix the cat enters a time machine and travels back to the time of the dinosaurs, where he spends the rest of his life hunting small reptiles. According to the doctrine of existential inertia, objects have a blockable tendency to continue existing.

Question: If Felix has existential inertia, was his inertial tendency to continue existing blocked at noon when he time-traveled to the past, and hence failed to exist past today’s noon?

My intuition is that the answer is negative. Existential inertia seems to me to be about “having a future” and today at noon, Felix does have a future, even if that future is in the distant past. In other words, if there is such a thing as existential inertia, it concerns what I call “internal” rather than “external” time.

Beyond mere intuition, here is a reason for a defender of existential inertia to agree with me. If existential inertia concerns external time, then in a relativistic world it is a doctrine that says that an object that exists at point z of spacetime has a tendency to exist somewhere or other in the forwards lightcone centered on z. But there is something odd about a metaphysical principle, like existential inertia is supposed to be, that impels an object to continue to exist in some location or other in some infinite set of locations (say, the infinite number of locations in the forward lightcone one second away from the present in some reference frame), without impelling the object to exist in any particular location, or even imposing any kind of probability distribution on where it is to exist. Moreover, it is not clear why the forward lightcone would be so metaphysically special that a fundamental metaphysical principle would coordinate with lightcones so neatly.

Perhaps this is not completely convincing. But it has some legs. There is thus some reason to think that existential inertia applies to internal rather than external time. But if so, then existential inertia has not removed all that needs to be explained about persistence. For a normal cat not only tends to continue to exist in its internal-time future, but also tends to continue to exist in its external-time future, since normally there is no time travel. And this external-time persistence is not explained by existential inertia, if existential inertia concerns the external-time future. So there is a persistence to explain, and theism offers an explanation. There is still room for an argument for theism from persistence.

Here is a closely related explanatory problem: Why is it that internal and external time tend to be correlated, so that internal-time persistence tends to imply external-time persistence?

Suppose that, contrary to my relativity theory intuitions, one insists that existential inertia concerns external-time persistence rather than internal-time persistence? Then there is still something to be explained: the correlation between internal and external time.

Physicalism, persons, fission and eliminativism

People are philosophically unhappy about nonlocality in quantum mechanics. It is interesting to me that there is an eerily similar nonlocality on standard psychological theories of personal identity. For on those theories:

1. You survive if your memories survive in one living person.

2. You perish if your memories fission between more than one living person.

Now imagine that your brain is frozen, the data from it is destructively read, and then sent to two different stations, A and B, located in opposite directions five light minutes away from your original brain. At each station, a coin is simultaneously flipped (say, in the rest frame of your original brain). If it’s heads (!), the data is put into a freshly cloned brain in a vat, and if it’s tails, the data is deleted.

On a psychological theory, if both coins land heads you perish by (2). But if exactly one coin lands heads, you survive at that station. So whether you exist at one station depends on what happens simultaneously (according to one frame) at a station ten light minutes away.

Note, however, that this is not explicable via quantum nonlocality, because quantum nonlocality depends on entanglement, and there is no relevant entanglement in this thought experiment. It would be a nonlocality beyond physics.

I think one lesson here is that ostensibly physicalist or physicalist-friendly theories of persons or minds can end up sounding oddly dualist. For if dualism were true, it wouldn’t be utterly surprising if facts about where your soul reappears could have a faster-than-light dependence on far away events, since souls aren’t governed by the laws of physics. Similarly, on functionalism plus psychological theories of personal identity, you could move between radically different physical embodiments or even between a physical embodiment and a nonphysical realization. That, too, sounds rather like what you would expect dualism to say.

If I were a physicalist, I would perhaps be inclined to be drawn by these observations towards eliminativism about persons. For these observations suggest that even physicalist pictures of the person may be too deeply influenced by the dualist roots of philosophical and theological reflection on personhood. If these roots are seen as intellectually corrupt by the physicalist, then it should be somewhat attractive to deny the existence of persons.

Internal reference frame

Suppose a long snake is stretched out and its front half is annihilated instantaneously. This presumably instantly destroys the snake's form or soul. So the tip of the snake's tail instantly ceases to be informed by the snake form. But then there will be a reference frame according to which the front half is annihilated before the tail loses its form. In that frame, the tip of the tail still has a snake form at a time at which the snake's front half doesn't exist. That seems wrong. So it seems there should be a privilege to reference frames where the front half is destroyed simultaneously with the tail losing its form. But a global privileged frame is unattractive. Maybe, however, we should suppose that particular substances carry along privileged frames of their own, frames internal to them. Then there will be a privilege frame for each substance, but these frames need not cohere into a global privileged frame.

Accidents outlasting their substance

At least as traditionally philosophically understood, the Catholic understanding of transsubstantiation insists on the persistence of (at least some) of the accidents of bread and wine after the bread and wine have ceased to exist. But how can accidents exist without their substance?

Well, imagine a very long rattlesnake—say, a billion kilometers long—all stretched out in space. Suppose that the snake rattles its rattle at noon for a second, and one second after the end of the rattling a prearranged array of blasters simultaneously annihilates the whole snake.

Let R be the accident of the snake's rattling. A simple relativistic calculation shows that there is an inertial reference frame in which the rattling occurs after the vast majority of the snake—including all of the snake's vital organs (which I assume are placed much as in a normal snake)—has been annihilated. But an animal is dead, and hence non-existent (barring afterlife for animals; let's stipulate there is none), after all its vital organs have been annihilated. Thus, there is a reference frame in which the accident R exists after the substance S of the snake has been annihilated.

So special relativity gives us good reason to think that accidents can survive the destruction of the substance, at least in some inertial reference frames. But all inertial reference frames are supposed to be on par.

I suppose an opponent of transsubstantiation could insist that while an accident can survive the destruction of a substance in some reference frames, it cannot survive the destruction of the substance in all reference frames (as it would have to in the case of the Eucharist). But that requirement sounds a little ad hoc.

So, relativity theory gives us good reason to reject one of the most famous objections to transsubstantiation.

Special relativity and the A-theory

I've been thinking about (Special) Relativity Theory and the A-theory of time. The A-theory of time requires an absolute simultaneity. Relativity theory seems to deny an absolute simultaneity.

But need it? Why not instead say this? Relativity theory never even talks about simultaneity. It talks about a different relation: simultaneity relative to a frame. Likewise, relativity theory never talks about spatial or temporal distances. It talks about spatial or temporal distances relative to a frame. These are different concepts: simultaneity, spatial distance and temporal distance are binary relations. Simultaneity relative to a frame, spatial distance relative to a frame and temporal distnace relative to a frame are ternary relations (the frame is a relatum). All the stuff Relativity says about simultaneity relative to a frame, spatial distance relative to a frame and temporal distnace relative to a frame may very well be true. But the A-theorist need not worry at all about this, because that's not what she is talking about.

But wouldn't it follow, then, that contrary to relativity theory there is a privileged reference frame? There are two questions here: (a) Does it follow that there is a privileged reference frame? (b) Would this be contrary to relativity theory? And neither question has a clearly positive answer.

The standard answer to (a) is this. If we have absolute simultaneity and a Minkowski spacetime, then we can define a privileged frame as the inertial frame whose simultaneity relation matches the absolute simultaneity relation. But nothing that was said so far guarantees that any inertial frame has a simultaneity relation that matches our absolute simultaneity relation. Suppose, for instance, that there are two points, a and b, that are absolutely simultaneous but where b is in the forward light-cone of a. Then not only will there be no inertial frame according to which a and b are simultaneous, but there won't be any foliation by spacelike hypersurfaces (which I guess could be our General Relativistic version of a reference frame) according to which they are simultaneous. Granted, that would be weird. But so far nothing has ruled this out. To get a positive answer to (a) we would need a posit that bridges between metaphysics and physics, namely that the absolute simultaneity relation agrees with the simultaneity relation of some frame.

What about (b)? Is it contrary to Relativity for there to be a privileged reference frame? It surely depends on the way in which the frame is privileged. Suppose, for instance, that earth is the only inhabited planet in the universe. Then the reference frame of the earth is privileged as the reference frame of the reference frame of the only inhabited planet in the universe. While earth may not be the only inhabited planet in the universe, it is no business of Relativity Theory to decide that question. So it had better not be contrary to Relativity for one reference frame to be privileged in this way.

Now, it is essential to Einstein's project that no reference frame be privileged with respect to the fundamental laws of nature. But I don't see that the A-theorist need hold anything that implies some reference frame is privileged in this way. The fundamental laws of motion, perhaps, talk only about what moves relative to reference frames, and say nothing about what moves simpliciter.

If the answer to (a) is positive, then presumably our A-theorist should hold that there is no metaphysically privileged reference frame. But Einstein's Principle of Relativity appears to be a (second-order) law of physics rather than a law of metaphysics. Why should we read it as denying a metaphysically privileged frame? Granted, Einstein so read it. But did he have reason to assert such a strengthened Principle?

All that said, while there is no incoherence between the A-theory and Relativity Theory, I think there is a plausibilistic argument from Relativity against the A-theory. On any sensible A-theory, the events that appear commonsensically simultaneous are at least approximately simultaneous, and the events that appear commonsensically far from simultaneous are not simultaneous. Moreover, our normal commonsensical measurements of distance (with meter sticks) and time (with clocks) had better approximately match up with the correct absolute distance and absolute time measurements. Now, these ordinary life judgments and measurements match up with those provided by our Relativistic science, relative to some reasonable reference frame. Such a match would be a surprising and vast coincidence if there were no deeper connection between absolute simultaneity, distance and time and simultaneity, distance and time according to a frame.

So, it seems that if we are to have a sensible A-theory, we will want to say that there is some frame whose simultaneity relation at least approximately matches absolute simultaneity, and likewise for temporal and spatial difference. But this sort of global coincidence is precisely the sort of thing for laws of nature to explain. So our sensible A-theorist should have fundamental laws of nature that entail that there is a frame whose simultaneity and distance relations approximately match the absolute ones. But these laws will violate Einstein's strictures against the laws not privileging a frame. For such laws privilege those frames whose relativized relations approximately match the absolute ones over those frames where this does not happen. And so such laws are improbable by Einstein's inductive argument for the Principle of Relativity.

There is also a perhaps more direct argument. On the supposition that there is an absolute simultaneity relation, it is surprising that frames whose simultaneity relation do and do not match are treated equally in the laws of motion. On the supposition that there is no such simultaneity relation, there is no surprise there. So, the laws of motion favor there not being an absolute simultaneity relation in a familiar Bayesian way.

How fat am I?

Suppose I think of myself as shaped like a four-dimensional spacetime worm. We draw diagrams of such things for students—a wide line moving up the board. It is amusing to note that such diagrams are not at all to scale. In a natural unit system, the speed of light will be taken to be c=1. For instance, one might measure time in seconds and distance in in light-seconds. A light second is 299792458 meters long. An average human earthly lifespan is of the order of magnitude of 10⁹ seconds. My largest spatial dimension is about two meters, i.e., about 10⁻⁸ light-seconds. That means that my earthly temporal dimension is of the order of magnitude 10¹⁷ times longer than my largest spatial dimension. This means that I thought of as a spacetime worm, I am an exceedingly thin worm. If this worm were rotated, projected and scaled so as to be a meter long and maximally thick, a hydrogen atom would be ten million times thicker than the worm.

Moreover, this worm is quite straight. The main variation in its shape seems to be a cork-screw shape induced by the earth's orbit around the sun. But the diameter of the spiral is about a thousand light-seconds, which is a millionth of its length.

So a scale drawing of me in my earthly career as a space-time worm would have me be 10¹⁷ times thinner than I am long, and despite a subtle cork-screw, straight to within about one part per million.

A problem with Special Relativity Theory for perdurantists

There seems to be a problem for the conjunction of Special Relativity and perdurantism.  Maybe this is a standard problem that has a standard solution? Let's say that being bent is an intrinsic property. Perdurantists of the sort I am interested in think that Socrates is bent at a time in virtue of an instantaneous temporal part of him being bent (I think the argument can be made to work with thin but not instantaneous parts, but it's a little more complicated). Therefore:

1. x is bent at t only if the temporal part of x at t is bent simpliciter.

The following also seems like something perdurantists should say:

2. x is bent simpliciter only if every temporal part of x is bent simpliciter.

Now, we need to add some premises about the interaction of Special Relativity and time.

3. There is a one-to-one correspondence between times and maximal spacelike hypersurfaces such that one exists at a time if and only if one at least partly occupies the corresponding hypersurface.

Given a time t, let H(t) be the corresponding maximal spacelike hypersurface. And if h is a maximal spacelike hypersurface, then let T(h) be the corresponding time. Write P(x,t) for the temporal part of x at t. Then:

4. P(x,t) is wholly contained within H(t) and if z is a spacetime point in H(t) and within x, then z is within P(x,t)

and, plausibly:

5. If a point within x is within a maximal spacelike hypersurface h, then P(x,T(h)) exists.

Now suppose we have Special Relativity, so we're in a Minkowski spacetime. Then:

6. For any point z in spacetime, there are three maximal spacelike hypersurfaces h₁, h₂ and h₃ whose intersection contains no points other than z.

Add this obvious premise:

7. No object wholly contained within a single spacetime point is bent simpliciter.

Finally, for a reductio, suppose:

8. x is an object that is bent at t.

Choose a point z within P(x,t) and choose three spacelike hypersurfaces h₁, h₂ and h₃ whose intersection contains z and only z (by 6). Now define the following sequence of objects, which exist by 4 and 5:

• x₁=P(x,t)
• x₂=P(x₁,T(h₁))
• x₃=P(x₂,T(h₂))
• x₄=P(x₃,T(h₃))

Observe that x₄ is wholly contained in the intersection of the three hypersurfaces h₁, h₂ and h₃, and hence:

9. x₄ is wholly at z.
10. It is not the case that x₄ is bent simpliciter.

Now:

11. x₁ is bent simpliciter. (By 1 and 8)
12. x₂ is bent simpliciter. (By 2 and 11)
13. x₃ is bent simpliciter. (By 2 and 12)
14. x₄ is bent simpliciter. (By 2 and 13)

Since 14 contradicts 10, we have a problem.  It seems the perdurantist cannot have any objects that are bent at any time in a Minkowski spacetime. This is a problem for the perdurantist. If I were a perdurantist, I'd deny 2, and maintain that an object can be bent simpliciter despite having temporal parts that are bent and temporal parts that are not bent. But I would not be comfortable with maintaining this. I would take this to increase the cost of perdurantism. What is ironic here is that it is often thought that endurantism is what has trouble with Relativity.